Sec 5.6 Quadratic Formula & Discriminant

Quadratic Formula (Yes, it’s the one with the song!) If ax 2 + bx + c = 0 and a ≠ 0, then the solutions (roots) are: Use the quadratic formula when you can’t factor to solve a quadratic equation The solutions are the x-intercepts (zeros) of the parabola

Examples 1.x 2 + 5x – 14 = 0 a=1, b=5, c=-14 OR

2.x 2 – 7x + 6 = 0

3.4x 2 = 8 – 3x

Discriminant: b 2 – 4ac The discriminant tells you how many solutions and what type you will haveThe discriminant tells you how many solutions and what type you will have If positive: 2 real solutions If negative: 2 imaginary solutions If zero: 1 real solution

Examples Find the discriminant and give the number and type of solutions.Find the discriminant and give the number and type of solutions. a.9x 2 + 6x + 1 = 0 a=9, b=6, c=1 a=9, b=6, c=1 b 2 – 4ac = (6) 2 – 4(9)(1) =36 – 36 = 0 1 real solution b.x 2 – 6x + 10 = 0 c. x 2 – 6x + 8 = 0